I always read it differently.
[…] Wyrds, capable of receiving or siphoning Arc from a source and redirecting it without loss of power. Theurges […] shape Arc into powerful effects, given the proper physical medium capable of holding a charge. […] the only limitation is physical contact with the specially crafted material that acts as a vehicle for their power. […] Like Theurges, Warcasters can channel Arc and manipulate its shape and effects […] And like a Wyrd, the Warcaster can transmit Arc over distance.
(The Thousand Worlds, pp. 15–16)
Warcasters basically are Theurges as well as Wyrds. They can manipulate Arc both ways, but nothing suggests they are more powerful doing it when they are directly operating on the battlefield (e.g. see Master Tulcan).
What makes them more powerful is the Rack itself:
Rack – A Warcaster coordinates and supports their forces from a sophisticated command and control center called a rack, located on the bridge of their battle carrier. In addition to the Warcaster’s multitude of displays and communications equipment, the rack also monitors and facilitates the Warcaster’s ability to channel Arc and contains multiple Cypher modules that can be activated at will.
(The Thousand Worlds, pp. 245–246)
Cypher module – An arcane-coded mechanika construct that, when charged with Arcanessence by a Warcaster, can invoke a Cypher. Most battle force units are equipped with one or more Cypher modules. Warcasters typically customize their racks with an array of Cypher modules that can be channeled to their units on the battlefield or through skilled wyrds under their command.
(The Thousand Worlds, p. 243)
[…] The plexus also enables its wearer to be empowered by the various performance-enhancing arcane Cyphers that their Warcaster may activate from their rack during battle.
(The Thousand Worlds, p. 245)
The rack and its Cypher modules are what make a Warcaster powerful. But still, a Warcaster can only operate when within Arc range:
[…] Safely housed within the battle carrier’s command rack, the Warcaster could charge her vehicle’s mechanika with vital Arcanessence, […] but only while within Arc range.
(The Thousand Worlds, p. 232)
Suddenly, the Razorbat’s Arc receivers awakened. The arcane mechanika enmeshed within the vehicle’s weapons and onboard systems pulsed with energy that could only be infused by one of the rarest of individuals capable of conducting Arcanessence. Fiddler knew she was in Arc range of her Warcaster.
(The Thousand Worlds, p. 234)
I assume the Arc range is represented as a battle carrier’s “channeling range”. If this is correct, it means that the battle carrier increases the Warcaster’s Arc range manyfold, adding to a Warcaster’s perceived power.
Venger Battle Carrier […] Warcaster Rack: 15x Cypher Modules […] Channeling Range: 5.2 miles
(The Thousand Worlds, pp. 76–77)
Iron Clad Battle Carrier […] Warcaster Rack: 15x Cypher Modules […] Channeling Range: 3.2 miles
(The Thousand Worlds, pp. 108–109)
Leviathan Battle Carrier […] Warcaster Rack: 15x Cypher Modules […] Channeling Range: 4.1 miles
(The Thousand Worlds, pp. 134–135)
In summary, rather than Warcasters themselves being so powerful, that they are kept safe in a battle carrier’s rack, the advanced mechanika of the rack makes the Warcaster that powerful in the first place.